The prospect of a special-election loss in yet another seat this week is fueling calls for House Republicans to radically shift course – or face losses in November that could lock their party in the minority for a generation.

Strike two: A Democrat wins a May 3 vote in a Louisiana congressional district that President Bush in 2004 carried by a 19-point margin.

Tuesday's runoff election in Mississippi's First Congressional District could be strike three. Democrat Travis Childers already nearly defeated Republican Greg Davis in an April 22 special election to replace GOP Rep. Roger Wicker, falling just 410 votes short of a majority. The idea that a Democrat could win the runoff has shocked national party leaders into overdrive.

"This seat is a very important one. It's been in conservative hands for a long time, and we'd hate to see the liberals gain control," said Vice President Dick Cheney in a phone interview released by the White House. The vice president is headlining a get-out-the-vote rally for Mr. Davis in Mississippi on Monday.

Citing recent special-election losses, former House Speaker Newt Gingrich issued a "Plea to Republicans" last week. "Without change we could face a catastrophic election this fall," he wrote in the conservative weekly Human Events. "Without change the Republican Party in the House could revert to the permanent minority status it had from 1930 to 1994."

This week House Republican leader John Boehner, who has been predicting a tough election for months, launches the long rollout of a new messaging campaign that has been dubbed by some party aides a "rebranding exercise."

For Republicans, the past 15 months have been mainly about "defining the Democrats," he says, citing their "very liberal agenda" and broken promises – especially the "Pelosi premium," a reference to House Speaker Nancy Pelosi's failure to deliver on a promise to bring down high gasoline prices.

But the need now is for Republicans to get clear on their own agenda for change, says Representative Boehner. "While we'll continue to hold Democrats accountable, I think it's also time for us to define ourselves, in terms of what we would do if the American people would honor us with the majority," he said in a May 8 briefing .

"We can't just be against everything the Democrats are trying to do. We have to be for a positive agenda," says Rep. Darrell Issa (R) of California, a member of the new panel. "Bad times are a problem for those who are in charge. The 'Pelosi premium' is that the price of a barrel of oil has doubled since she said: 'Elect me and I have a plan to reduce the power of oil.' "

Even before special-election setbacks this spring, House Republicans faced a tough campaign. With nearly 1 in 8 in the GOP caucus retiring or running for higher office, Republicans are defending 25 open seats compared with Democrats' seven open seats. Analysts say Democrats stand a good shot at winning many of them.

Even with rebranding, "the fact is there's a lot that House Republicans just can't change," says David Wasserman, who analyzes House races for the Cook Political Report in Washington. "They can't do a lot about these Republicans who are retiring."

House Republicans also face shortfalls in fundraising, especially from within their own ranks. The Democratic Congressional Campaign Committee has raised $44.3 million for the 2008 races, compared with $7.2 million for the National Republican Congressional Committee (NRCC), the House GOP campaign arm.

Last week, House GOP leaders warned colleagues in a closed meeting that if they didn't step up fundraising for the party, losses in November could be severe.

"To be competitive, the members of the Republican conference must continue to support this institution [the NRCC] with their energy and resources," says NRCC spokesman Ken Spain.

In a May 3 memo, the NRCC said the lesson from the Louisiana special-election defeat is that last-minute ads linking Democrat Don Cazayoux with Speaker Pelosi and Sen. Barack Obama helped Davis gain "substantial ground." "This election speaks to the potential toxicity of an Obama candidacy and the possible drag he could have down-ballot this fall," the NRCC memo said.

But some Republicans say a strategy of linking Democrats to Pelosi and Obama will fail. "People are tired of President Bush and they want a change. You can see it by the turnout and fundraising for the Democrats," says retiring Rep. Ray LaHood (R) of Illinois.

"Every special election has its ... local elements to it, but when you start to lose a succession of seats that have been solidly Republican ... that's a big warning sign," says Norman Ornstein, senior fellow at the American Enterprise Institute.